BIB-VERSION:: CS-TR-v2.0
          ID:: STAN//CS-TR-79-774
       ENTRY:: June 19, 1995
ORGANIZATION:: Stanford University, Department of Computer Science
       TITLE:: Large scale geodetic least squares adjustment by dissection
               and orthogonal decomposition
        TYPE:: Technical Report
      AUTHOR:: Golub, Gene H.
      AUTHOR:: Plemmons, Robert J.
        DATE:: November 1979
       PAGES:: 40
    ABSTRACT:: Very large scale matrix problems currently arise in the
               context of accurately computing the coordinates of points on
               the surface of the earth. Here geodesists adjust the
               approximate values of these coordinates by computing least
               squares solutions to large sparse systems of equations which
               result from relating the coordinates to certain observations
               such as distances or angles between points. The purpose of
               this paper is to suggest an alternative to the formation and
               solution of the normal equations for these least squares
               adjustment problems. In particular, it is shown how a
               block-orthogonal decomposition method can be used in
               conjunction with a nested dissection scheme to produce an
               algorithm for solving such problems which combines efficient
               data management with numerical stability. As an indication of
               the magnitude that these least squares adjustment problems
               can sometimes attain, the forthcoming readjustment of the
               North American Datum in 1983 by the National Geodetic Survey
               is discussed. Here it becomes necessary to linearize and
               solve an overdetermined system of approximately 6,000,000
               equations in 400,000 unknowns - a truly large-scale matrix
               problem.
       NOTES:: [Adminitrivia V1/Prg/19950619]
         END:: STAN//CS-TR-79-774